Question

Find the sum of the first 24 terms of the sequence when nth term is given by an=3+2/3n​

Answer 1

Step-by-step explanation:

Given

Sn = 3n² + 5n

n'th term = 164

To find

the value of m

Solution

\sf \implies S_1 = a_1 = 3(1)^2 + 5(1) = 8⟹S

1

=a

1

=3(1)

2

+5(1)=8

\sf \implies S_2 =3(2)^2 + 5(2) = 22⟹S

2

=3(2)

2

+5(2)=22

\sf \implies S_2 = 22 = a_1+a_2⟹S

2

=22=a

1

+a

2

\sf\implies a_2 = 22 - 8 = 14⟹a

2

=22−8=14

\sf \implies d = a_2 - a_1 = 14-8=6⟹d=a

2

−a

1

=14−8=6

\sf \implies {n}^{th}\: term = 164, \ then \: value \: of \: m?⟹n

th

term=164, thenvalueofm?

\sf \implies {n}^{th} \: term = a+(m-1)d⟹n

th

term=a+(m−1)d

\sf \implies 164 = 8+(m-1)6⟹164=8+(m−1)6

\sf \implies \dfrac{164-8}{6} =m-1⟹

6

164−8

=m−1

\sf \implies \dfrac{156}{6} =m-1⟹

6

156

=m−1

\sf \implies 26 =m-1⟹26=m−1

\sf \implies m= 26+1⟹m=26+1

\sf \implies m = 27⟹m=27

Therefore, 27ᵗʰ term is 164.

Hope it helps